Skip to main content
SpringerLink
Log in

Establish the Expected Number of Injective Motifs on Unlabeled Graphs Through Analytical Models

  • Conference paper
  • First Online:
Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 882))

Included in the following conference series:

Abstract

Network motifs have a central role in explaining the functionality of complex systems. Establishing motif significance requires the computation of the expected number of their occurrences according to a random graph model. Few models have been proposed to analytically derive the expected number of non-induced occurrences of a motif. In this paper we present an analytical model to compute the expected number of occurrences of induced motifs in unlabeled graphs. We will illustrate two different algorithms for computing the occurrence probability of induced motifs. We evaluate the performance of our algorithms for calculating the expected number of induced motifs with up to 10 nodes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://konect.cc.

References

  1. Chen, J., Yuan, B.: Detecting functional modules in the yeast protein-protein interaction network. Bioinformatics 22(18), 2283–2290 (2006)

    Article  Google Scholar 

  2. Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Proc. Natl. Acad. Sci. 99(25), 15879–15882 (2002)

    Article  MathSciNet  Google Scholar 

  3. Daudin, J.J., Picard, F., Robin, S.: A mixture model for random graphs. Stat. Comput. 18(2), 173–183 (2008)

    Article  MathSciNet  Google Scholar 

  4. Erdos, P., Renyi, A.: On random graphs. Publ. Math. 6, 290–297 (1959)

    MathSciNet  MATH  Google Scholar 

  5. Johnson, N.L., Kotz, S., Kemp, A.W.: Univariate Discrete Distributions. Wiley (1992)

    Google Scholar 

  6. Kocay, W.: An extension of Kelly’s lemma to spanning subgraphs. Congr. Numer. 31, 109–120 (1981)

    MathSciNet  MATH  Google Scholar 

  7. Micale, G., Giugno, R., Ferro, A., Mongiovì, M., Shasha, D., Pulvirenti, A.: Fast analytical methods for finding significant labeled graph motifs. Data Min. Knowl. Discov. 32(2), 1–28 (2018)

    Article  MathSciNet  Google Scholar 

  8. Micale, G., Pulvirenti, A., Ferro, A., Giugno, R., Shasha, D.: Fast methods for finding significant motifs on labelled multi-relational networks. J. Complex Netw. cnz008 (2019)

    Google Scholar 

  9. Milo, R., Kashtan, N., Itzkovitz, S., et al.: On the uniform generation of random graphs with prescibed degree sequences. Cond. Mat. 0312028, 1–4 (2004)

    Google Scholar 

  10. Milo, R., Shen-Orr, S., Itzkovitz, S., et al.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)

    Article  Google Scholar 

  11. Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)

    Article  Google Scholar 

  12. Nowicki, K., Snijders, T.: Estimation and prediction for stochastic block structures. J. Am. Stat. Assoc. 96, 1077–1087 (2001)

    Article  Google Scholar 

  13. Park, J., Newman, M.: The origin of degree correlations in the Internet and other networks. Phys. Rev. E 68, 026112 (2003)

    Article  Google Scholar 

  14. Picard, F., Daudin, J.J., Koskas, M., et al.: Assessing the exceptionality of network motifs. J. Comput. Biol. 15(1), 1–20 (2008)

    Article  MathSciNet  Google Scholar 

  15. Prill, R., Iglesias, P.A., Levchenko, A.: Dynamic properties of network motifs contribute to biological network organization. PLoS Biol. 3(11), e343 (2005)

    Article  Google Scholar 

  16. Shen-Orr, S.S., Milo, R., Mangan, S., et al.: Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet. 31, 64–68 (2002)

    Article  Google Scholar 

  17. Squartini, T., Garlaschelli, D.: Analytical maximum-likelihood method to detect patterns in real networks. New J. Phys. 13(8), 083001 (2011)

    Article  Google Scholar 

  18. Wernicke, S.: Efficient detection of network motifs. IEEE/ACM Trans. Comput. Biol. Bioinf. 3(4), 347–359 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Catania, Catania, Italy

    Emanuele Martorana

  2. Department of Clinical and Experimental Medicine, University of Catania, Catania, Italy

    Giovanni Micale, Alfredo Ferro & Alfredo Pulvirenti

Authors
  1. Emanuele Martorana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giovanni Micale
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alfredo Ferro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alfredo Pulvirenti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfredo Pulvirenti .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Martorana, E., Micale, G., Ferro, A., Pulvirenti, A. (2020). Establish the Expected Number of Injective Motifs on Unlabeled Graphs Through Analytical Models. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_21

Download citation

Publish with us

Policies and ethics

Search

Navigation